Problem: Given $ m \angle BOC = 9x + 46$, and $ m \angle AOB = 4x - 22$, find $m\angle AOB$. $O$ $A$ $C$ $B$
Solution: From the diagram, we see that together ${\angle AOB}$ and ${\angle BOC}$ form ${\angle AOC}$ , so $ {m\angle AOB} + {m\angle BOC} = {m\angle AOC}$ Since $\angle AOC$ is a straight angle, we know ${m\angle AOC = 180}$ Substitute in the expressions that were given for each measure: $ {4x - 22} + {9x + 46} = {180}$ Combine like terms: $ 13x + 24 = 180$ Subtract $24$ from both sides: $ 13x = 156$ Divide both sides by $13$ to find $x$ $ x = 12$ Substitute $12$ for $x$ in the expression that was given for $m\angle AOB$ $ m\angle AOB = 4({12}) - 22$ Simplify: $ {m\angle AOB = 48 - 22}$ So ${m\angle AOB = 26}$.